Origins of the helical wrapping of phenyleneethynylene polymers about single-walled carbon nanotubes

The highly charged, conjugated polymer poly[p-{2,5-bis(3-propoxysulfonicacidsodiumsalt)}phenylene]ethynylene (PPES) has been shown to wrap single-wall carbon nanotubes (SWNTs), adopting a robust helical superstructure. Surprisingly, PPES adopts a helical rather than a linear conformation when adhered to SWNTs. The complexes formed by PPES and related polymers upon helical wrapping of a SWNT are investigated using atomistic molecular dynamics (MD) simulations in the presence and absence of aqueous solvent. In simulations of the PPES/SWNT system in an aqueous environment, PPES spontaneously takes on a helical conformation. A potential of mean force, ΔA(ξ), is calculated as a function of ξ, the component of the end-to-end vector of the polymer chain projected on the SWNT axis; ξ is a monotonic function of the polymer's helical pitch. ΔA(ξ) provides a means to quantify the relative free energies of helical conformations of the polymer when wrapped about the SWNT. The aqueous system possesses a global minimum in ΔA(ξ) at the experimentally observed value of the helical pitch. The presence of this minimum is associated with preferred side chain conformations, where the side chains adopt conformations that provide van der Waals contact between the tubes and the aliphatic components of the side chains, while exposing the anionic sulfonates for aqueous solvation. The simulations provide a free energy estimate of a 0.2 kcal/mol/monomer preference for the helical over the linear conformation of the PPES/SWNT system in an aqueous environment.